The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) -semigroups. In 1981, Sen [8] has introduced the concept of the -semigroups. We can see that any semigroup can be considered as a -semigroup. The concept of ordered ideal extensions in ordered -semigroups was introduced in 2007 by Siripitukdet and Iampan [12]. Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered -semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered -semigroups.